Problem: Divide the following complex numbers: $\dfrac{5(\cos(\frac{13}{12}\pi) + i \sin(\frac{13}{12}\pi))}{\cos(\frac{1}{12}\pi) + i \sin(\frac{1}{12}\pi)}$ (The dividend is plotted in blue and the divisor in plotted in green. Your current answer will be plotted orange.)
Solution: Dividing complex numbers in polar forms can be done by dividing the radii and subtracting the angles. The first number ( $5(\cos(\frac{13}{12}\pi) + i \sin(\frac{13}{12}\pi))$ ) has angle $\frac{13}{12}\pi$ and radius 5. The second number ( $\cos(\frac{1}{12}\pi) + i \sin(\frac{1}{12}\pi)$ ) has angle $\frac{1}{12}\pi$ and radius 1. The radius of the result will be $\frac{5}{1}$ , which is 5. The angle of the result is $\frac{13}{12}\pi - \frac{1}{12}\pi = \pi$ The radius of the result is $5$ and the angle of the result is $\pi$.